The Method of Fundamental Solutions for Three-Dimensional Nonlinear Free Surface Flows Using the Iterative Scheme
Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(8), 1715; https://doi.org/10.3390/app9081715
Received: 22 March 2019 / Revised: 11 April 2019 / Accepted: 22 April 2019 / Published: 25 April 2019
(This article belongs to the Special Issue Advances in Geohydrology: Methods and Applications)
In this article, we present a meshless method based on the method of fundamental solutions (MFS) capable of solving free surface flow in three dimensions. Since the basis function of the MFS satisfies the governing equation, the advantage of the MFS is that only the problem boundary needs to be placed in the collocation points. For solving the three-dimensional free surface with nonlinear boundary conditions, the relaxation method in conjunction with the MFS is used, in which the three-dimensional free surface is iterated as a movable boundary until the nonlinear boundary conditions are satisfied. The proposed method is verified and application examples are conducted. Comparing results with those from other methods shows that the method is robust and provides high accuracy and reliability. The effectiveness and ease of use for solving nonlinear free surface flows in three dimensions are also revealed.